If the ratio of cats to dogs is 2:3, how many dogs are there if there are 10 cats?

To determine the number of dogs given the ratio of cats to dogs is 2:3 and there are 10 cats, it's essential to understand what this ratio means. The ratio of 2:3 signifies that for every 2 cats, there are 3 dogs.

First, we can set up a relation based on the number of cats. If we let the number of cats be represented by the part of the ratio that corresponds to the cats (which is 2), then we can express it mathematically:

Let the number of cats be represented as (2x) and the number of dogs as (3x).

We know that there are 10 cats, which can be expressed as:

[2x = 10]

To find (x), we divide both sides by 2:

[x = 5]

Now that we have the value of (x), we can find the number of dogs using the dogs' part of the ratio, (3x):

[3x = 3 \times 5 = 15]

Thus, the total number of dogs is 15, confirming that when there are 10 cats, there are 15 dogs corresponding to the ratio of